Analysis of the light extraction efficiency of light-emitting diodes with photonic crystals combined with the generalized Rouard method

The light extraction efficiency of light-emitting diodes (LEDs) patterned with photonic crystals is investigated based on an incoherent multi-reflection-transmission model. The formulas of the extraction efficiency are obtained in an analytic form similar to the unpatterned case. Besides, we generalize the Rouard formulas commonly used in thin-film optics to the case of multilayered photonic crystal slabs. The influence of various types of backside reflectors and the absorption of the semiconductor on the efficiency are demonstrated for GaN-based LEDs. The optimization of the photonic crystal slab based on the LED model is also presented and briefly discussed. (C) 2009 Optical Society of AmericaOpticsSCI(E)22289-2962